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New two‐dimensional slope limiters for discontinuous Galerkin methods on arbitrary meshes
Author(s) -
Hoteit H.,
Ackerer Ph.,
Mosé R.,
Erhel J.,
Philippe B.
Publication year - 2004
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1172
Subject(s) - discontinuous galerkin method , polygon mesh , limiter , mathematics , piecewise , quadratic equation , conservation law , limiting , piecewise linear function , mathematical analysis , geometry , finite element method , computer science , physics , engineering , mechanical engineering , telecommunications , thermodynamics
In this paper, we introduce an extension of Van Leer's slope limiter for two‐dimensional discontinuous Galerkin (DG) methods on arbitrary unstructured quadrangular or triangular grids. The aim is to construct a non‐oscillatory shock capturing DG method for the approximation of hyperbolic conservative laws without adding excessive numerical dispersion. Unlike some splitting techniques that are limited to linear approximations on rectangular grids, in this work, the solution is approximated by means of piecewise quadratic functions. The main idea of this new reconstructing and limiting technique follows a well‐known approach where local maximum principle regions are defined by enforcing some constraints on the reconstruction of the solution. Numerical comparisons with some existing slope limiters on structured as well as on unstructured meshes show a superior accuracy of our proposed slope limiters. Copyright © 2004 John Wiley & Sons, Ltd.